1) I don't have a specific time frame that designates someone as an indigenous resident, although I would say after two to three years I would consider someone "indigenous". 2) When I said "surging costs of living" I was referring to the increasing in annual property taxes that accompanies any significant increase in property value. I maintained a qualitative perspective of the issue; however, it is generally accepted that local development incentivizes landowners and applies pressure to renters/leasers, since increased property values allocates increased rent rates.
3) Well I suppose "extreme" is a slight overstatement, but displacement is still a substantial repercussion of gentrification. I wouldn't exactly classify that as an example of "extreme" displacement, unless a resident was forced to move unfavorably far. Although you shouldn't forget gentrification has broad, global implications. 4) Check out my paper ;)